Optimal Kernel Design for Finite-Element Numerical Integration on GPUs

2020 ◽  
Vol 22 (6) ◽  
pp. 61-74
Author(s):  
Krzysztof Banas ◽  
Filip Kruzel ◽  
Jan Bielanski
Keyword(s):  
Finite Element ◽  
Numerical Integration ◽  
Optimal Kernel ◽  
Kernel Design

Dynamic Analysis of Shipping Cask Subjected to Sequential Bolt Preload and Impact Loads

2009 ◽  
Author(s):  
Tsu-te Wu
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Numerical Integration ◽  
Dynamic Responses ◽  
Integration Scheme ◽  
Impact Loads ◽  
Element Mesh ◽  
Bolt Preload ◽  
Numerical Integration Scheme ◽  
Structural Responses

This paper presents an improved methodology for evaluating the dynamic responses of shipping casks subjected to the sequential HAC impact loads. The methodology utilizes the import technique of the finite-element mesh and the analytical results form one dynamic analysis using explicit numerical integration scheme into another dynamic analysis also using explicit numerical integration scheme. The new methodology presented herein has several advantages over conventional methods. An example problem is analyzed to illustrate the application of the present methodology in evaluating the structural responses of a shipping cask to the sequential HAC loading.

scholarly journals A Comprehensive Evaluation of Graph Kernels for Unattributed Graphs

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 984 ◽  
Author(s):  
Yi Zhang ◽  
Lulu Wang ◽  
Liandong Wang
Keyword(s):  
Comprehensive Evaluation ◽  
Classification Problem ◽  
Evaluation Framework ◽  
Graph Classification ◽  
Open Problems ◽  
Graph Kernels ◽  
Different Dimensions ◽  
Synthetic Datasets ◽  
Optimal Kernel ◽  
Kernel Design

Graph kernels are of vital importance in the field of graph comparison and classification. However, how to compare and evaluate graph kernels and how to choose an optimal kernel for a practical classification problem remain open problems. In this paper, a comprehensive evaluation framework of graph kernels is proposed for unattributed graph classification. According to the kernel design methods, the whole graph kernel family can be categorized in five different dimensions, and then several representative graph kernels are chosen from these categories to perform the evaluation. With plenty of real-world and synthetic datasets, kernels are compared by many criteria such as classification accuracy, F1 score, runtime cost, scalability and applicability. Finally, quantitative conclusions are discussed based on the analyses of the extensive experimental results. The main contribution of this paper is that a comprehensive evaluation framework of graph kernels is proposed, which is significant for graph-classification applications and the future kernel research.

Simulation of Piping Ratcheting Experiments Using Advanced Plane-Stress Cyclic Elastoplasticity Models

2019 ◽  
Author(s):  
Konstantinos Chatziioannou ◽  
Yuner Huang ◽  
Spyros A. Karamanos
Keyword(s):  
Finite Element ◽  
Numerical Integration ◽  
Plane Stress ◽  
Numerical Scheme ◽  
Large Scale ◽  
Low Cycle Fatigue ◽  
Structural Response ◽  
Material Behavior ◽  
Repeated Loading ◽  
Cycle Fatigue

Abstract Industrial steel piping components are often subjected to severe cyclic loading conditions which introduce large inelastic strains and can lead to low-cycle fatigue. Modeling of their structural response requires the simulation of material behavior under strong repeated loading, associated with large strain amplitudes of alternate sign. Accurate numerical predictions of low-cycle fatigue depend strongly on the selection of cyclic-plasticity model in terms of its ability to predict accurately strain at critical location and its accumulation (referred to as “ratcheting”). It also depends on the efficient numerical integration of the material model within a finite element environment. In the context of von Mises metal plasticity, the implementation of an implicit numerical integration scheme for predicting the cyclic response of piping components is presented herein, suitable for large-scale structural computations. The constitutive model is formulated explicitly for shell-type (plane-stress) components, suitable for efficient analysis of piping components whereas the numerical scheme has been developed in a unified manner, allowing for the consideration of a wide range of hardening rules, which are capable of describing accurately strain ratcheting. The numerical scheme is implemented in a general-purpose finite element software as a material-user subroutine, with the purpose of analyzing a set of large-scale physical experiments on elbow specimens undergoing constant-amplitude in-plane cyclic bending. The accuracy of three advanced constitutive models in predicting the elbow response, in terms of both global structural response and local strain amplitude/accumulation, is validated by direct comparison of numerical results with experimental data, highlighting some key issues associated with the accurate simulation of multiaxial ratcheting phenomena. The very good comparison between numerical and experimental results, indicates that the present numerical methodology and, in particular, its implementation into a finite element environment, can be used for the reliable prediction of mechanical response of industrial piping elbows, under severe inelastic repeated loading.

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bruna Caroline Campos ◽  
Felício Bruzzi Barros ◽  
Samuel Silva Penna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Numerical Integration ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Content Type ◽  
Integration Techniques ◽  
Integration Strategies ◽  
Element Method

Purpose The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered. Design/methodology/approach Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results. Findings Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities. Originality/value This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

Large Deformation Analysis of the Arterial Cross Section

1971 ◽  
Vol 93 (2) ◽  
pp. 138-145 ◽  
Author(s):  
B. R. Simon ◽  
A. S. Kobayashi ◽  
D. E. Strandness ◽  
C. A. Wiederhielm
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Numerical Integration ◽  
Density Function ◽  
Cross Section ◽  
Finite Deformation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Exponential Form ◽  
Strain Energy Density Function

Possible relations between arterial wall stresses and deformations and mechanisms contributing to atherosclerosis are discussed. Necessary material properties are determined experimentally and from available data in the literature by assuming the arterial response to be a static finite deformation of a thick-walled cylinder constrained in a state of plane strain and composed of an incompressible, nonlinear elastic, transversely isotropic material. Experimental justification from the literature and supporting theoretical considerations are presented for each assumption. The partial derivative of the strain energy density function δW1/δI , necessary for in-plane stress calculation, is determined to be of exponential form using in situ biaxial test results from the canine abdominal aorta. An axisymmetric numerical integration solution is developed and used as a check for finite element results. The large deformation finite element theory of Oden is modified to include aortic material nonlinearity and directional properties and is used for a structural analysis of the aortic cross section. Results of this investigation are: (a) Fung’s exponential form for the strain energy density function of soft tissues is found to be valid for the aorta in the biaxial states considered; (b) finite deformation analyses by the finite element method and numerical integration solution reveal that significant tangential stress gradients are present in arteries commonly assumed to be “thin-walled” tubes using linear theory.

scholarly journals Numerical integration on the sphere

1982 ◽  
Vol 23 (3) ◽  
pp. 332-347 ◽  
Author(s):  
Kendall Atkinson
Keyword(s):  
Finite Element ◽  
Numerical Integration ◽  
Potential Theory ◽  
Double Layer ◽  
Unit Sphere ◽  
Gaussian Quadrature ◽  
Integration Methods ◽  
Numerical Integration Methods ◽  
Element Type ◽  
Surface Integrals

AbstractThis is a discussion of some numerical integration methods for surface integrals over the unit sphere in R3. Product Gaussian quadrature and finite-element type methods are considered. The paper concludes with a discussion of the evaluation of singular double layer integrals arising in potential theory.

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